The invention relates to digital image compression and interpolation.
In digital image processing, the image is encoded and processed as an array of pixel intensities. To improve the image so that it is more suitable for a particular application various enhancement techniques are available to process the digitally encoded image. The enhancement techniques fall into two general categories, namely, frequency-domain methods and spatial-domain methods. The first category typically involves modifying the Fourier transform of the image; whereas, the latter category typically involves manipulation of pixels in the image.
The basis of the frequency domain methods is the convolution theorem. That is, the original image is convolved with a position-invariant operator to form another image. It can be shown that this operation is equivalent to multiplying the Fourier transform of the image function by the Fourier transform of the operator, also sometimes referred to as the transfer function. The transfer function is generally selected to accentuate some important features of the image, for example, the high frequency components which are associated with edge detail.
In contrast, spatial-domain methods generally define an aggregate of pixels, also referred to as a subimage, centered at some location (x,y) of the image. An operator is then applied to the subimage as the center of the subimage is moved from pixel to pixel of the larger image. For example, the operator could compute a weighted average of the pixels surrounding the location (x,y), in which case, the operator would be performing a smoothing operation. Such smoothing operations are typically used to diminish the effects of noise in the original image.